Calculation method, calculation apparatus and program

ABSTRACT

The present disclosure enables vehicle dispatch in consideration of individual differences of each orderer for a price and a required time by a computer executing an input procedure to input parameters for a distance matrix relating to a distance between a taxi and an orderer giving a taxi dispatch order, a travel distance for an order, an opportunity cost parameter for a taxi driver, and an acceptance probability function of the orderer, and a calculation procedure to calculate a price and a required time to be presented to the orderer by solving an optimization problem formulated using the parameters.

TECHNICAL FIELD

The present invention relates to a calculation method, a calculationapparatus, and a program.

BACKGROUND ART

In recent years, in the mobile service by taxi, IT has been promotedsuch that vehicle dispatch applications become widespread, and so on. Asa result, people's movement history can be obtained, so that a pricesetting of a mobile service is made for each region, and prediction ofmobile demand and the like are made.

There are many researches on techniques involved in the vehicle dispatchtechniques and price determination techniques to maximize the profits oftaxi. Examples include a price determination technique in accordancewith the mobile demand in each region (NPL 2), minimization of thetravel distance of taxi in an idle state (NPL 1), and the like.

In order to make a simultaneous determination of a price and time takinginto account the probability of acceptance of an individual, it isnecessary to solve a two-step optimization problem includinguncertainties. Solutions to such an optimization problem include theL-shaped method, a technique combining an implicit enumeration methodand the L-shaped method, and the like.

CITATION LIST Non Patent Literature

NPL 1: Nandani Garg and Sayan Ranu. Route recommendations for idle taxidrivers: Find me the shortest route to a customer! In Proceedings of the24th ACM SIGKDD International Conference on Knowledge Discovery & #38,Data Mining, KDD '18, pp. 1425{1434, New York, N.Y., USA, 2018.ACM.

NPL 2: Yongxin Tong, Libin Wang, Zimu Zhou, Lei Chen, Bowen Du, andJieping Ye. Dynamic pricing in spatial crowdsourcing: A matching-basedapproach. In SIGMOD Conference, 2018.

SUMMARY OF THE INVENTION Technical Problem

However, vehicle dispatch has not yet been carried out in considerationof the characteristics of each orderer. For example, nearby taxis arepreferentially dispatched for busy people, and distant taxis are cheaplydispatched for less busy people, and so on. In order to carry out such avehicle dispatch method, it is necessary to model and consider theacceptance or rejection of orderers according to the taxi price and therequired time of each orderer when formulating the vehicle dispatchplan.

The present invention has been made in view of the circumstancesdescribed above, and an object of the present invention is to enablevehicle dispatch in consideration of individual differences of eachorderer for the price and the required time.

Means for Solving the Problem

In order to solve the above problem, a computer executes: an inputprocedure to input parameters for a distance matrix relating to adistance between a taxi and an orderer giving a taxi dispatch order, atravel distance for an order, an opportunity cost parameter for a taxidriver, and an acceptance probability function of the orderer; and acalculation procedure to calculate a price and a required time to bepresented to the orderer by solving an optimization problem formulatedusing the parameters.

Effects of the Invention

The present invention enables vehicle dispatch in consideration ofindividual differences of each orderer for the price and the requiredtime.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a diagram illustrating an example of a system assumed in anembodiment of the present invention.

FIG. 2 is a diagram illustrating an example of a hardware configurationof a calculation apparatus 10 according to the embodiment of the presentinvention.

FIG. 3 is a diagram illustrating an example of a functionalconfiguration of the calculation apparatus 10 according to theembodiment of the present invention.

FIG. 4 is a flowchart for illustrating an example of a processingprocedure performed by the calculation apparatus 10.

FIG. 5 is a flowchart for illustrating an example of the processingprocedure of a calculation process of a presented price and a presentedtime.

DESCRIPTION OF EMBODIMENTS

Existing techniques have not been able to take account of the taxiacceptance probability of individuals for the price and the requiredtime. For example, the problem formulated in NPL 2 can be written asfollows.

First, suppose that orderers of vehicle dispatch of taxis r_(i) (i=1, 2,. . . , n) and drivers of taxis w_(j) (j=1, 2, . . . , m) are present inthe space. Each driver can only dispatch to an orderer within a radiusaw from its position, and E is a set of combinations of orderers anddrivers that can be dispatched. It is assumed that each orderer i has adistance d_(i) from the getting-in place of the order to the getting-offplace. It is also assumed that the space is divided into grids g=1, 2, .. . , 1, and the orderers present in each grid g accept the proposalwith a probability of S_(g) (p_(g)) and reject the proposal with aprobability of 1−S_(g) (p_(g)) for the price p_(g) per unit of taxidistance presented to each. The acceptance probability determinesacceptance or rejection, and by using the result, it is possible toconstruct a bipartite graph regarding the orderers and the drivers thatcan be matched. If a ∈ {0, 1}^(n) represents the acceptance result ofeach orderer, a_(i)=1 represents acceptance and a_(i)=0 representsrejection for each orderer i. For each acceptance result a, a matchingproblem between taxis and orderers to maximize the corporate profits canbe written as follows.

$\begin{matrix}\left\lbrack {{Math}.1} \right\rbrack &  \\{{\max\limits_{z}{\sum\limits_{i,j}{p_{gi}d_{i}a_{i}z_{ij}}}}\begin{matrix}{{s.t.\text{}{\sum\limits_{j}z_{ij}}} \leq 1} & \left( {{i = 1},2,\ldots,n} \right) \\{{\sum\limits_{i}z_{ij}} \leq 1} & \left( {{j = 1},2,\ldots,m} \right) \\{z_{ij} \in \left\{ {0,1} \right\}} & \left( {\forall{\left( {i,j} \right) \in E}} \right)\end{matrix}} & \end{matrix}$

where, g_(i) is a subscript representing the grid in which the orderer iexists. z_(ij) represents the matching of the orderer i and the taxi j,and if z_(ij)=1, the taxi j is dispatched to the orderer i. p_(gi)d_(i)in the objective function represents the profit when matching isestablished. If z_(ij)=1 and a_(i)=1, matching is established, resultingin the profit of p_(gi)d_(i). However, if z_(ij)=0 or a_(i)=0, matchingis not established, so the profit is 0. The first constraint is to limitthe number of taxis that can be dispatched to an orderer to one, and thesecond constraint is to limit the number of orderers undertaken by ataxi to one. The fourth constraint is a constraint that only taxis thatcan be dispatched within the time presented to the orderer can bedispatched to the orderer.

Thus, the problem of maximizing the expected value of the profitobtained by presenting the price vector p of all grids to the customercan be written as follows when the optimal value of the above problem ish (a, p).

$\begin{matrix}\left\lbrack {{Math}.2} \right\rbrack &  \\{{\max\limits_{p}{E\left\lbrack {h\left( {a,p} \right)} \middle| p \right\rbrack}} = {\sum\limits_{a \in {\{{0,1}\}}^{n}}{P{r\left( a \middle| p \right)}{h\left( {a,p} \right)}}}} & (2)\end{matrix}$ where $\begin{matrix}\left\lbrack {{Math}.3} \right\rbrack &  \\{{\Pr\left( {\left. a \middle| p \right.,t} \right)}:={\prod\limits_{{i = 1},2,\ldots,n}{\left\{ {{S_{gi}\left( p_{gi} \right)}^{a_{i}}\left( {1 - {S_{gi}\left( p_{gi} \right)}} \right)^{({1 - a_{i}})}} \right\}.}}} & (3)\end{matrix}$

However, in this approach, the acceptance probability for the price isdefined for each region, and the difference in the acceptanceprobability of each orderer is not taken into consideration. Changes inthe acceptance probability according to the required time is also notcaptured. Thus, in the present embodiment, the optimization problem isformulated in consideration of the acceptance probability of individualsfor the price and the required time.

However, the problem formulated according to the present embodiment isdifficult to solve with conventional techniques. Conventional techniquessuch as the L-shaped method, which is a conventional technique foroptimization problems including uncertainties, and a technique combiningan implicit enumeration method and the L-shaped method cannot be appliedto the problem of the present embodiment, and the optimization problemincluding the probability model with time and price as elements asdescribed above is very difficult to solve with the following twopoints.

-   Because 2^(n) of bipartite graph matching is included in the    objective function, the calculation of the derivative value and the    objective function value cannot be performed in polynomial time.-   The objective function is discontinuous with respect to t.

It is possible to obtain a local optimal solution by using a gradientmethod or the like by solving the second-stage problem for all casescaused by the probability, but it requires a huge amount of calculationtime. Thus, in the present embodiment, an approximate solution(approximate algorithm) with a small amount of calculation that takesadvantage of the unique characteristics of the problem is proposed forthe formulated problem.

Formulation of Optimization Problem Including Acceptance ProbabilityModel of Orderer for Price and Time

The problem of the present embodiment is formulated. First, as apremise, each orderer i has an acceptance probability S_(i) (p, t) for acase where a taxi of a price p and a required time t (the time fromordering to the arrival of the taxi at the getting-in place+the time tofulfill the order of the orderer (i.e., travel time to the getting-offplace)) is presented. The orderer determines whether to take a taxiaccording to this acceptance probability. Examples of such an acceptanceprobability model include a discrete choice model using a generalizedcost function. Additionally, various probability models can be utilized,such as logistic regression models and deep learning models. Theacceptance probability model also includes acceptance probability modelsaccording to each region of conventional techniques, so it can beadopted.

A case where a discrete choice model using a generalized cost functionis used as an acceptance probability model will be described. First, thegeneralized cost is the total cost of travel converted into monetaryvalue. For example, the generalized cost C_(ik) when the individual iselects the means of transportation k can be defined as follows usingthe price p_(k) of the means of transportation k, the time t_(k)required for the traveling, and the time value W_(i), which is themonetary value per unit time.

C _(ik) =p _(k) +W _(i) t _(k)

At this time, the probability that the orderer i selects the means oftransportation k′ can be defined as follows using a generalized costfunction, where K is the set of options for the means of transportation.

P _(ik′) =Pr(C _(ik )+ε_(k′) <C _(ik)+ε_(k)|∀k ∈ K/{k′})

where, ε is a random variable representing an error, and represents theinfluence of other factors that cannot be grasped by the monetary costand the time cost or the influence of the estimation error of the timevalue W. Assuming that each E is independent of each other and follows aGumbel distribution having the same distribution, the probability thatthe individual i selects the option k′ is derived as follows.

$\begin{matrix}\left\lbrack {{Math}.4} \right\rbrack &  \\{P_{{ik}^{\prime}} = {\frac{\exp\left( {- C_{{ik}^{\prime}}} \right)}{\sum_{k \in K}{\exp\left( {- C_{ik}} \right)}} = \frac{\exp\left( {{- p_{k^{\prime}}} - {W_{i}t_{k^{\prime}}}} \right)}{\sum_{k \in K}{\exp\left( {{- p_{k}} - {W_{i}t_{k}}} \right)}}}} & \end{matrix}$

Thus, the probability that the individual i selects a taxi with a pricep and a required time t is derived as follows.

$\begin{matrix}\left\lbrack {{Math}.5} \right\rbrack &  \\{{S_{i}\left( {p,t} \right)} = \frac{\exp\left( {p + {W_{i}t}} \right)}{{\exp\left( {p + {W_{i}t}} \right)} + {\sum_{k \in K}{\exp\left( {p_{k} + {W_{i}t_{k}}} \right)}}}} & \end{matrix}$

where, K represents a set of options for the means of transportationother than taxis. Here, because public transportation (trains, buses,etc.) has published prices and required times, the prices and requiredtimes of other means of transportation, p_(k), t_(k), can be input fromexternal information. The time value parameter W_(i) of each orderer ican be estimated from acceptance history data of taxis or the like, soit is possible to set the acceptance probability model.

The problem is formulated using the above assumptions. Suppose thatorderers r_(i) (i=1, 2, . . . , n) and drivers w_(j) (j=1, 2, . . . , m)are present in the space as illustrated on the left side of FIG. 1 . Atthis time, if the price p_(i) and the required time t_(i) are presentedto each orderer i, suppose that each orderer i accepts the proposal witha probability of S_(i) (p_(i), t_(i)), and rejects the proposal with aprobability of 1−S_(i) (p_(i), t_(i)).

In this way, the acceptance probability determines acceptance orrejection, and as a result, it is possible to construct a bipartitegraph regarding the orderers and the drivers that can be matched. Theright side of FIG. 1 is a bipartite graph illustrating the orderers andthe drivers that can be matched when the price and the required time arepresented in the state on the left side. In this example, the orderer r₂rejects the proposal, so there is no edge connecting to the node of r₂.Because the driver w₃ cannot fulfill the order within the presented timefor the orderer r 1, there is no edge connecting r₁ and w₃.

Here, a ∈ {0, 1}^(n) represents the acceptance result of each orderer.a_(i)=1 represents acceptance and a_(i)=0 represents rejection for eachorderer i. When the price p and the time t are presented to n orderersand the result of acceptance or rejection is represented by a, thematching problem between taxis and orderers to maximize the corporateprofits can be written as follows.

$\begin{matrix}\left\lbrack {{Math}.6} \right\rbrack &  \\{{\max\limits_{z}{\sum\limits_{i,j}{\left( {p_{i} - {\alpha\left( {c_{ij} + d_{i}} \right)}} \right)a_{i}z_{ij}}}}\begin{matrix}{{s.t.\text{}{\sum\limits_{j}z_{ij}}} \leq 1} & \left( {{i = 1},2,\ldots,n} \right) \\{{\sum\limits_{i}z_{ij}} \leq 1} & \left( {{j = 1},2,\ldots,m} \right) \\{z_{ij} = 0} & \left( {t_{i} < {c_{ij} + d_{i}}} \right) \\{z_{ij} \in \left\{ {0,1} \right\}} & \left( {\forall\left( {i,j} \right)} \right)\end{matrix}} & (2)\end{matrix}$

z_(ij) represents the matching of the orderer i and the taxi j, and ifz_(ij)=1, the taxi j is dispatched to the orderer i. a represents theopportunity cost per unit time of the taxi driver, c_(ij) represents thetime required for the taxi j to arrive at the departure place of theorderer i, and d_(i) represents the time from the departure place(getting-in place) of the orderer i to the destination place(getting-off place), and (p_(i)-α(c_(ij)+d_(i))) in the objectivefunction represents the profit when matching is established. If z_(ij)=1and a_(i)=1, matching is established, resulting in the profit of(p_(i)−α(c_(ij)+d_(i))). However, if z_(ij)=0 or a_(i)=0, matching isnot established, so the profit is 0.

The first constraint is to limit the number of taxis that can bedispatched to an orderer to one, and the second constraint is to limitthe number of orderers undertaken by a taxi to one. The fourthconstraint is a constraint that only taxis that can fulfill the orderwithin the time presented to the orderer can be dispatched to theorderer. When the optimal value of the problem (2) is f (a, p, t), theexpected value of the profit obtained by presenting p, t to the customeris

$\begin{matrix}\left\lbrack {{Math}.7} \right\rbrack &  \\{{\max\limits_{p,t}{E\left\lbrack {\left. {f\left( {a,p,t} \right)} \middle| p \right.,t} \right\rbrack}} = {\sum\limits_{a \in {\{{0,1}\}}^{n}}{{\Pr\left( {{a❘p},t} \right)}{{f\left( {a,p,t} \right)}.}}}} & (3)\end{matrix}$ Here, $\begin{matrix}\left\lbrack {{Math}.8} \right\rbrack &  \\{{\Pr\left( {\left. a \middle| p \right.,t} \right)}:={\prod\limits_{{i = 1},2,\ldots,n}{\left\{ {{S_{i}\left( {p_{i},t_{i}} \right)}^{a_{i}}\left( {1 - {S_{i}\left( {p_{i}\ ,t_{i}} \right)}} \right)^{({1 - a_{i}})}} \right\}.}}} & \end{matrix}$

Thus, it is sufficient to find p, t to maximize this, but there are alsothe following constraints for p, t.

[Math. 9]

S_(i)(p_(i), t_(i))≥C (i=1, 2, . . . , n)   (4)

C is a constant that satisfies C E [0, 1]. This is a constraintcondition not to present an exorbitant amount to each orderer. Withoutthis constraint, if the number of orderers is extremely large for thenumber of drivers, for example, in the event of terrorism or a disaster,the phenomenon of raising the price will occur. Raising the price in theevent of an incident such as terrorism or a disaster can be a majorbashing target, so it is necessary to incorporate such a constraint. Bysetting C=0, this constraint can be removed.

The problem to be solved can be formulated as the following optimizationproblem.

$\begin{matrix}\left\lbrack {{Math}.10} \right\rbrack &  \\{{\max\limits_{p,t}{\sum\limits_{a \in {\{{0,1}\}}^{n}}{{\Pr\left( {\left. a \middle| p \right.,t} \right)}{f\left( {a,p,t} \right)}}}}{{s.t.{S_{i}\left( {p_{i},t_{i}} \right)}} \geq {C\left( {{i = 1},2,\ldots,n} \right)}}} & (5)\end{matrix}$

The formulation in the present embodiment is consistent with theformulation in conventional techniques by providing the followingsettings and constraints. By adopting the acceptance probability modelaccording to each region of conventional techniques as the acceptanceprobability model, and defining α=0, C=0, and the presented requiredtime t_(i) as the sum of the time required for the driver to travel thedistance a_(w) and the time required to fulfill the order, the problem(5) is consistent with the problem setting of the conventionaltechniques. Thus, the formulation in the present embodiment hasincreased the degree of freedom of formulation according to theconventional techniques.

Hereinafter, an embodiment of the present invention will be describedwith reference to the drawings. FIG. 2 is a diagram illustrating anexample of a hardware configuration of a calculation apparatus 10according to the embodiment of the present invention. The calculationapparatus 10 of FIG. 2 includes a drive device 100, an auxiliary storagedevice 102, a memory device 103, a CPU 104, an interface device 105, adisplay device 106, an input device 107, and the like, which areconnected to each other through a bus B.

A program that realizes processing in the calculation apparatus 10 isprovided on a recording medium 101 such as a CD-ROM. When the recordingmedium 101 having the program stored therein is set in the drive device100, the program is installed in the auxiliary storage device 102 fromthe recording medium 101 via the drive device 100. However, the programdoes not necessarily have to be installed from the recording medium 101,and may be downloaded from another computer via a network. The auxiliarystorage device 102 stores the installed program and also storesnecessary files, data, and the like.

The memory device 103 reads and stores the program from the auxiliarystorage device 102 when the program is instructed to start. The CPU 104realizes a function relevant to the calculation apparatus 10 inaccordance with the program stored in the memory device 103. Theinterface device 105 is used as an interface for connection to anetwork. The display device 106 displays a graphical user interface(GUI) or the like based on the program. The input device 107 isconfigured with a keyboard, a mouse, and the like and is used forinputting various operation instructions.

FIG. 3 is a diagram illustrating an example of a functionalconfiguration of the calculation apparatus 10 according to theembodiment of the present invention. In FIG. 3 , the calculationapparatus 10 includes an input unit 11, a formulation unit 12, anoptimization unit 13, an output unit 14, and the like. One or moreprograms installed in the calculation apparatus 10 cause the CPU 104 toexecute processing, thereby these units are achieved.

Hereinafter, a processing procedure that is executed by the calculationapparatus 10 will be described. FIG. 4 is a flowchart for describing anexample of the processing procedure performed by the calculationapparatus 10.

In step S101, the input unit 11 inputs each parameter of the problem(the distance matrix relating to distances between the taxis andorderers, the travel distance in each order, the opportunity costparameter of the taxi drivers, and the acceptance probability functionfor each orderer).

Subsequently, the formulation unit 12 makes a formulation to anoptimization problem based on the parameters input by the input unit 11(substituting the parameters into the optimization problem) (S102).Subsequently, the optimization unit 13 calculates the approximatesolutions p and tin the problem (5) based on the parameters of theproblem formulated by the formulation unit 12 (S103). Subsequently, theoutput unit 14 outputs the approximate solutions p and t calculated bythe optimization unit 13 (S104).

Subsequently, details of Step S103 will be described.

By solving the optimization problem (5), it is possible to determine theoptimal presented price and the required time. Any optimizationtechnique may be used as long as it is possible to derive an approximatesolution that achieves the optimal solution of the above-describedproblem or a good objective function value. For example, the solutionmay be determined by genetic algorithm, Bayesian optimization, or thelike, or an algorithm proposed in the future may be used.

However, the following approximate solution is proposed in the presentembodiment because there is no existing conventional technique that cansolve the optimization problem described above at high speed.

Approximate Solution

Consider the following problem as an approximation problem of theoptimization problem (5).

$\begin{matrix}\left\lbrack {{Math}.11} \right\rbrack &  \\\begin{matrix}\max\limits_{p,t} & {f\left( {{\sum\limits_{a \in {\{{0,1}\}}^{n}}{Pr\left( {\left. a \middle| p \right.,t} \right)a}},p,t} \right)} \\{s.t.} & {{S_{i}\left( {p_{i},t_{i}} \right)} \geq {C\left( {{i = 1},2,\ldots,n} \right)}}\end{matrix} & (6)\end{matrix}$ Intheproblem(5), $\begin{matrix}\left\lbrack {{Math}.12} \right\rbrack &  \\{\sum_{a \in {\{{0,1}\}}^{n}}{\Pr\left( {\left. a \middle| p \right.,t} \right)}} & \end{matrix}$

is external to the function f, whereas in the above problem,

Σ_(a∈{0,1}) _(n) Pr(a|p, t)   [Math. 13]

is internal to the function f By performing this operation, it ispossible to transform a problem in which a plurality of bipartite graphmatching exists into a problem dealing with one typical bipartite graphmatching problem.

In this case, assuming that the optimal value in the problem (5) is vand the optimal value in the problem (6) is v′, v and v′ have thefollowing feature.

$\begin{matrix}\left\lbrack {{Math}.14} \right\rbrack &  \\{v^{\prime} \leq v \leq {\frac{1}{C}v^{\prime}}} & \end{matrix}$

Thus, by solving the problem (6), an approximate solution of the problem(5) can be obtained.

The optimization unit 13 executes an algorithm utilizing this in stepS103. FIG. 5 is a flowchart illustrating an example of the processingprocedure of the calculation process of the presented price and thepresented time.

In step S201, the optimization unit 13 calculates

{circumflex over (p)} _(ij)=argmax {(p _(ij)−α(c _(ij) +d _(i)))S _(i)(p_(ij) , c _(ij))|S _(i)(p _(ij) , c _(ij))≥C}  [Math. 15]

for each edge (i, j) of the bipartite graph. The optimization unit 13also defines r_(j):=1 for each j. The optimization unit 13 also definesE:={(i, j)|i=1, 2, . . . , n, j=1, 2, . . . , m}. The optimization unit13 further determines the maximum number of iterations. The maximumnumber of iterations may be input by a user.

Subsequently, the optimization unit 13 solves the following optimizationproblem (S202).

$\begin{matrix}\left\lbrack {{Math}.16} \right\rbrack &  \\{{\max\limits_{z}{\sum\limits_{{({i,j})} \in E}{\left( {{\overset{\hat{}}{p}}_{ij} - {\alpha\left( {c_{ij} + d_{i}} \right)}} \right){S_{i}\left( {{\hat{p}}_{ij},c_{ij}} \right)}r_{j}z_{ij}}}}\begin{matrix}{{s.t.{\sum\limits_{j = 1}^{m}z_{ij}}} \leq 1} & \left( {{i = 1},2,\ldots,n} \right) \\{{\sum\limits_{i = 1}^{n}z_{ij}} \leq 1} & \left( {{j = 1},2,\ldots,m} \right) \\{z_{ij} \in \left\{ {0,1} \right\}} & \left( {\left( {i,j} \right) \in E} \right)\end{matrix}\ } & (7)\end{matrix}$

Subsequently, the optimization unit 13 determines the presented priceand the presented time based on the solution to the problem describedabove. The optimization unit 13 also updates the edge set E with theupdate rule (S203). Specifically, when the solution to the problemdescribed above is

{circumflex over (z)},   [Math. 17]

the optimization unit 13 defines

p_(i)={{circumflex over (p)}_(ij)|{circumflex over (z)}_(ij)=1},t_(i)={c_(ij)|{circumflex over (z)}_(ij)=1},   [Math. 18]

and updates the edge set E excluding the corresponding branch (i, j)from the edge set E to

E=E\{(i, j)|{circumflex over (z)}_(ij)=1}.   [Math. 19]

Subsequently, the optimization unit 13 determines conditions if

{circumflex over (z)}_(ij)=0,   [Math. 20]

for all (i, j), or if E=φ (empty set), or whether or not the number ofiterations (number of iterations after step S202) has reached themaximum number of iterations (S204). If the condition is satisfied (Yesat S204), the optimization unit 13 terminates the process in FIG. 5 .

On the other hand, in a case that the condition is not satisfied (No inS204), for

For each {(i, j)|{circumflex over (z)}_(ij)=1},   [Math. 21]

the optimization unit 13 updates r_(j) as

r _(j):=1−S _(i)({circumflex over (p)} _(ij) , c _(ij)),   [Math. 22]

and returns to step S202.

As described above, according to the present embodiment, by solving theproblem of determining the price and the time of the taxi inconsideration of the acceptance probability model that represents theacceptance or rejection of the orderer for the price and the requiredtime of the taxi for each orderer as a probability model, it is possibleto dispatch a vehicle in consideration of individual differences of eachorderer for the price and the required time. As a result, it is possibleto dispatch a vehicle according to the characteristics of eachindividual, and it is possible to improve corporate profits and theoverall social welfare of the orderers.

Note that, in the present embodiment, the optimization unit 13 is anexample of a calculation unit.

Although the embodiments of the present invention have been described indetail above, the present invention is not limited to such specificembodiments, and various modifications and changes can be made withoutdeparting from the gist of the present invention described in theaspects.

REFERENCE SIGNS LIST

-   10 Calculation apparatus-   11 Input unit-   12 Formulation unit-   13 Optimization unit-   14 Output unit-   100 Drive device-   101 Recording medium-   102 Auxiliary storage device-   103 Memory device-   104 CPU-   105 Interface device-   106 Display device-   107 Input device-   B Bus

1. A calculation method comprising, executed by a computer: receivinginput parameters for a distance matrix relating to a distance between ataxi and an orderer giving a taxi dispatch order, a travel distance foran order, an opportunity cost parameter for a taxi driver, and anacceptance probability function of the orderer; and calculating a priceand a required time to be presented to the orderer by solving anoptimization problem formulated using the input parameters.
 2. Thecalculation method according to claim 1, wherein the calculatingincludes solving the optimization problem with a discrete choice modelbased on a generalized cost function using the input parameters as anacceptance probability model.
 3. The calculation method according toclaim 1, wherein the calculating includes solving the optimizationproblem using an approximate solution transforming a problem in which aplurality of bipartite graph matching exists into a problem dealing withone bipartite graph matching problem.
 4. A calculation apparatuscomprising a processor configured to execute a method comprising:receiving input parameters for a distance matrix relating to a distancebetween a taxi and an orderer giving a taxi dispatch order, a traveldistance for an order, an opportunity cost parameter for a taxi driver,and an acceptance probability function of the orderer; and calculating aprice and a required time to be presented to the orderer by solving anoptimization problem formulated using the input parameters.
 5. Thecalculation apparatus according to claim 4, wherein the calculatingincludes solving the optimization problem with a discrete choice modelbased on a generalized cost function using the input parameters as anacceptance probability model.
 6. The calculation apparatus according toclaim 4, wherein the calculating includes solving the optimizationproblem using an approximate solution transforming a problem in which aplurality of bipartite graph matching exists into a problem dealing withone bipartite graph matching problem.
 7. A computer-readablenon-transitory recording medium storing computer-executable programinstructions that when executed by a processor cause a computer toexecute a method comprising: receiving input parameters for a distancematrix relating to a distance between a taxi and an orderer giving ataxi dispatch order, a travel distance for an order, an opportunity costparameter for a taxi driver, and an acceptance probability function ofthe orderer; and calculating a price and a required time to be presentedto the orderer by solving an optimization problem formulated using theinput parameters.
 8. The calculation method according to claim 1, themethod further comprising: causing, based on a response from the ordererwhether to accept the price and the required time, dispatch of the taxito the orderer based on the price and the required time.
 9. Thecalculation method according to claim 1, wherein a distance between thetaxi and the orderer is within a predetermined distance.
 10. Thecalculation method according to claim 1, wherein the acceptanceprobability function of the orderer represents a probability rate ofacceptance by the orderer of the taxi dispatch order based on the priceand the required time of the taxi.
 11. The calculation method accordingto claim 2, wherein the calculating includes solving the optimizationproblem using an approximate solution transforming a problem in which aplurality of bipartite graph matching exists into a problem dealing withone bipartite graph matching problem.
 12. The calculation apparatusaccording to claim 4, the processor further configured to execute amethod comprising: causing, based on a response from the orderer whetherto accept the price and the required time, dispatch of the taxi to theorderer based on the price and the required time.
 13. The calculationapparatus according to claim 4, wherein a distance between the taxi andthe orderer is within a predetermined distance.
 14. The calculationapparatus according to claim 4, wherein the acceptance probabilityfunction of the orderer represents a probability rate of acceptance bythe orderer of the taxi dispatch order based on the price and therequired time of the taxi.
 15. The calculation apparatus according toclaim 5, wherein the calculating includes solving the optimizationproblem using an approximate solution transforming a problem in which aplurality of bipartite graph matching exists into a problem dealing withone bipartite graph matching problem.
 16. The computer-readablenon-transitory recording medium according to claim 7, wherein thecalculating includes solving the optimization problem with a discretechoice model based on a generalized cost function using the inputparameters as an acceptance probability model.
 17. The computer-readablenon-transitory recording medium according to claim 7, wherein thecalculating includes solving the optimization problem using anapproximate solution transforming a problem in which a plurality ofbipartite graph matching exists into a problem dealing with onebipartite graph matching problem.
 18. The computer-readablenon-transitory recording medium according to claim 7, thecomputer-executable program instructions when executed further causingthe computer system to execute a method comprising: causing, based on aresponse from the orderer whether to accept the price and the requiredtime, dispatch of the taxi to the orderer based on the price and therequired time.
 19. The computer-readable non-transitory recording mediumaccording to claim 7, wherein a distance between the taxi and theorderer is within a predetermined distance.
 20. The computer-readablenon-transitory recording medium according to claim 7, wherein theacceptance probability function of the orderer represents a probabilityrate of acceptance by the orderer of the taxi dispatch order based onthe price and the required time of the taxi.